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arXiv:quant-ph/9710036 · Fortschritte der Physik

Time-Symmetrized Quantum Theory

Lev Vaidman A

Published Nov 1, 1998• 15 citations
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Abstract

A brief review of the time-symmetrized quantum formalism originated by Aharonov, Bergmann and Lebowitz is presented. Symmetry of various measurements under the time reversal is analyzed. Time-symmetrized counterfactuals are introduced. It is argued that the time-symmetrized formalism demonstrates novel profound features of quantum theory and that recent criticism of the formalism is unfounded.

DOI
10.1002/(sici)1521-3978(199811)46:6/8<729::aid-prop729>3.0.co;2-q

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Proceedings of the National Academy of Sciences•Feb 1, 1960•59 citations
A brief review of the time-symmetrized quantum formalism originated by Aharonov, Bergmann and Lebowitz is presented. Symmetry of various measurements under the time reversal is analyzed. Time-symmetrized counterfactuals are introduced. It is argued that the time-symmetrized formalism demonstrates novel profound features of quantum theory and that recent criticism of the formalism is unfounded.
Recently, several authors have criticized time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was the proof, which appeared in various forms, showing that counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with the standard quantum theory. I argue here that the apparent contradiction appears due to inappropriate usage of traditional time asymmetric approach to counterfactuals, and that the contradiction disappears when the problem is analyzed in terms of time-symmetric counterfactuals. I analyze various aspects of time-symmetry of quantum theory and defend the time-symmetrized formalism.
Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory (TSQT). L. Vaidman has responded to those objections by proposing a new kind of time-symmetrized counterfactual, which he has defined in two different ways. It is argued that both definitions are problematic, and that the ABL rule cannot in general be used counterfactually. In particular, it is shown that Vaidman's counterargument to the Sharp and Shanks inconsistency proof fails. However, it is possible to retain a meaningful counterfactual reading of the ABL rule in a limited special case. This special case, which falls under a class identified by Cohen and Hiley, is discussed from a time-symmetry standpoint.
Recently, several authors have criticized the time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was a proof, appearing in various forms, which showed that the counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with standard quantum theory. I argue here that the apparent contradiction is due to a logical error. I analyze the concept of counterfactuals in quantum theory and introduce time-symmetrized counterfactuals. These counterfactuals do not lead to any contradiction with the predictions of quantum theory. I discuss applications of time-symmetrized counterfactuals to several surprising examples and show the usefulness of the time-symmetrized quantum formalism.
Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory (TSQT). I distinguish between two different readings of the ABL rule, counterfactual and non-counterfactual, and confirm that TSQT advocate L. Vaidman is employing the counterfactual reading to which these authors object. Vaidman has responded to the objections by proposing a new kind of time-symmetrized counterfactual, which he has defined in two different ways. It is argued that neither definition succeeds in overcoming the objections, except in a special case previously noted by Cohen and Hiley. In addition, a connection is made between TSQT and Price's concept of `advanced action', which further supports the special case discussed.
Recently, several authors have criticized the time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was a proof, appearing in various forms, which showed that the counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with standard quantum theory. I, (Vaidman, 1996a, 1997) have argued that the apparent contradiction is due to a logical error and introduced consistent time-symmetrized quantum counterfactuals. Here I repeat my arguments defending the time-symmetrized quantum theory and reply to the criticism of these arguments by Kastner (1999).